Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Is there a point of $ \omega\sp *$ that sees all others?

Author: Neil Hindman
Journal: Proc. Amer. Math. Soc. 104 (1988), 1235-1238
MSC: Primary 04A20; Secondary 03E05, 54D35
MathSciNet review: 931732
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If the cardinal $ c$ of the continuum is singular and $ p$ is an ultrafilter on $ \omega $ of character $ c$, then there is an ultrafilter $ q$ on $ \omega $ which is not comparable to $ p$ in the Rudin-Keisler order.

References [Enhancements On Off] (What's this?)

  • [1] W. Comfort, Ultrafilters: an interim report, Surveys in General Topology, Academic Press, New York, 1980, pp. 33-54. MR 564099 (81a:54007)
  • [2] W. Comfort and S. Negrepontis, The theory of ultrafilters, Springer-Verlag, Berlin, 1974. MR 0396267 (53:135)
  • [3] D. Fremlin, Consequences of Martin's Axiom, Cambridge Univ. Press, Cambridge, 1984.
  • [4] K. Kunen, Weak $ P$-points in $ {N^ * }$, Topology, Vol. II, Colloq. Math. Soc. Janos Bolyai 23 (1980), 741-749. MR 588822 (82a:54046)
  • [5] J. van Mill, An introduction to $ \beta \omega $, Handbook of Set-Theoretic Topology (K. Kunen and J. Vaughan, eds.), North-Holland, Amsterdam, 1984. MR 776630 (86f:54027)
  • [6] W. Rudin, Homogeneity problem in the theory of Čech compactifications, Duke Math. J. 23 (1956), 409-419. MR 0080902 (18:324d)
  • [7] S. Shelah and M. Rudin, Unordered types of ultrafilters, Topology Proc. 3 (1978), 199-204. MR 540490 (80k:04002)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 04A20, 03E05, 54D35

Retrieve articles in all journals with MSC: 04A20, 03E05, 54D35

Additional Information

Keywords: Ultrafilters, Rudin-Keisler order
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society